Chapter 8.5, Problem 74E

To determine

Determine the equation of line that passes through the given two points also discuss the advantages and disadvantages of each method.

Answer to Problem 74E

The equation of line is $y=2x-3$ .

Explanation of Solution

Given:

The graph

  

By using point-slope formula, first find the slope us using two points

  $m=\frac{y_2-y_1}{x_2-x_1}$

Now use the formula $y-y_1=m\left(x-x_1\right)$

To simplify this formula then the line will be in slope intercept from $y=mx+b$

Use two point formulae ;

  $\begin{array}{l}y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\\ y-1=\frac{5-1}{4-2}\left(x-2\right)\\ y-1=2\left(x-2\right)\\ y=2x-3\end{array}$

The disadvantage of this formulae is these is are defined if slope is finite.